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Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces. (English) Zbl 1173.47051
The convex feasibility problem (CFP) of finding a point in the nonempty intersection ${\cap }_{i=1}^{N}{C}_{i}$ is considered, where $N\ge 1$ is an integer and the ${C}_{i}$’s are assumed to be convex closed subsets of a Banach space $E$. By using hybrid iterative methods, the authors prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, they apply their results for solving convex feasibility problems in Banach spaces.
##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 47H09 Mappings defined by “shrinking” properties 47N10 Applications of operator theory in optimization, convex analysis, programming, economics 90C25 Convex programming